TY - JOUR

T1 - Operator Norm-Based Statistical Linearization to Bound the First Excursion Probability of Nonlinear Structures Subjected to Imprecise Stochastic Loading

AU - Ni, Peihua

AU - Jerez, Danko J.

AU - Fragkoulis, Vasileios C.

AU - Faes, Matthias G.R.

AU - Valdebenito, Marcos A.

AU - Beer, Michael

N1 - Funding Information: Peihua Ni and Michael Beer acknowledge the support from the German Research Foundation under Grant Nos. BE 2570/7-1 and MI 2459/1-1. Danko Jerez acknowledges the support from ANID (National Agency for Research and Development, Chile) and DAAD (German Academic Exchange Service) under CONI-CYT-PFCHA/Doctorado Acuerdo Bilateral DAAD Becas Chile/ 2018-6218007. Vasileios Fragkoulis gratefully acknowledges the support from the German Research Foundation under Grant No. FR 4442/2-1. Matthias Faes acknowledges the financial support of the Research Foundation Flanders (FWO) under postdoctoral Grant No. 12P3519N, as well as the Alexander von Humboldt foundation. Marcos Valdebenito acknowledges the support by ANID under its program FONDECYT, Grant No. 1180271.

PY - 2022/3

Y1 - 2022/3

N2 - This paper presents a highly efficient approach for bounding the responses and probability of failure of nonlinear models subjected to imprecisely defined stochastic Gaussian loads. Typically, such computations involve solving a nested double-loop problem, where the propagation of the aleatory uncertainty has to be performed for each realization of the epistemic parameters. Apart from near-trivial cases, such computation is generally intractable without resorting to surrogate modeling schemes, especially in the context of performing nonlinear dynamical simulations. The recently introduced operator norm framework allows for breaking this double loop by determining those values of the epistemic uncertain parameters that produce bounds on the probability of failure a priori. However, the method in its current form is only applicable to linear models due to the adopted assumptions in the derivation of the involved operator norms. In this paper, the operator norm framework is extended and generalized by resorting to the statistical linearization methodology to account for nonlinear systems. Two case studies are included to demonstrate the validity and efficiency of the proposed approach.

AB - This paper presents a highly efficient approach for bounding the responses and probability of failure of nonlinear models subjected to imprecisely defined stochastic Gaussian loads. Typically, such computations involve solving a nested double-loop problem, where the propagation of the aleatory uncertainty has to be performed for each realization of the epistemic parameters. Apart from near-trivial cases, such computation is generally intractable without resorting to surrogate modeling schemes, especially in the context of performing nonlinear dynamical simulations. The recently introduced operator norm framework allows for breaking this double loop by determining those values of the epistemic uncertain parameters that produce bounds on the probability of failure a priori. However, the method in its current form is only applicable to linear models due to the adopted assumptions in the derivation of the involved operator norms. In this paper, the operator norm framework is extended and generalized by resorting to the statistical linearization methodology to account for nonlinear systems. Two case studies are included to demonstrate the validity and efficiency of the proposed approach.

KW - Imprecise probabilities

KW - Operator norm theorem

KW - Statistical linearization

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85121543232&partnerID=8YFLogxK

U2 - 10.1061/AJRUA6.0001217

DO - 10.1061/AJRUA6.0001217

M3 - Article

AN - SCOPUS:85121543232

VL - 8

JO - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering

JF - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering

SN - 2376-7642

IS - 1

M1 - 04021086

ER -